def get_matrices():
dv = .001
nsyn_bg = 1
bgfr = 200
we = .1
wi = -.1
nsyn_00, nsyn_01, nsyn_10, nsyn_11 = 5, 5, 2, 20
# Components:
b0 = ExternalPopulation(bgfr, record=True)
i0 = InternalPopulation(tau_m=.05,
v_min=0,
v_max=1,
dv=dv,
update_method='gmres')
i1 = InternalPopulation(tau_m=.05,
v_min=0,
v_max=1,
dv=dv,
update_method='gmres')
b0_i0 = Connection(b0, i0, nsyn_bg, weights=we, delays=0.0)
b0_i1 = Connection(b0, i1, nsyn_bg, weights=we, delays=0.0)
i0_i0 = Connection(i0, i0, nsyn_00, weights=we, delays=0.0)
i0_i1 = Connection(i0, i1, nsyn_01, weights=we, delays=0.0)
i1_i0 = Connection(i1, i0, nsyn_10, weights=wi, delays=0.0)
i1_i1 = Connection(i1, i1, nsyn_11, weights=wi, delays=0.0)
L = get_leak_matrix(i1)
Se, te = get_connection_flux_matrices(b0_i0)
Si, _ = get_connection_flux_matrices(i1_i0)
return L, Se, Si, te
def get_matrices():
dv = .001
nsyn_bg = 1
bgfr = 200
we = .1
wi = -.1
nsyn_00, nsyn_01, nsyn_10, nsyn_11 = 5, 5, 2, 20
# Components:
b0 = ExternalPopulation(bgfr, record=True)
i0 = InternalPopulation(tau_m=.05, v_min=0, v_max=1, dv=dv, update_method = 'gmres')
i1 = InternalPopulation(tau_m=.05, v_min=0, v_max=1, dv=dv, update_method = 'gmres')
b0_i0 = Connection(b0, i0, nsyn_bg, weights=we, delays=0.0)
b0_i1 = Connection(b0, i1, nsyn_bg, weights=we, delays=0.0)
i0_i0 = Connection(i0, i0, nsyn_00, weights=we, delays=0.0)
i0_i1 = Connection(i0, i1, nsyn_01, weights=we, delays=0.0)
i1_i0 = Connection(i1, i0, nsyn_10, weights=wi, delays=0.0)
i1_i1 = Connection(i1, i1, nsyn_11, weights=wi, delays=0.0)
L = get_leak_matrix(i1)
Se, te = get_connection_flux_matrices(b0_i0)
Si, _ = get_connection_flux_matrices(i1_i0)
return L, Se, Si, te
def test_access_matrices():
i1 = InternalPopulation(v_min=0, v_max=.02, dv=.0001)
c1 = Connection(None, i1, 1, weights=.005)
leak_matrix = get_leak_matrix(i1)
synaptic_matrix, threshold_vector = get_connection_flux_matrices(c1)
assert leak_matrix.shape == synaptic_matrix.shape
assert synaptic_matrix.shape[0] == threshold_vector.shape[0]
def test_access_matrices():
i1 = InternalPopulation(v_min=0, v_max=.02, dv=.0001)
c1 = Connection(None, i1, 1, weights=.005)
leak_matrix = get_leak_matrix(i1)
synaptic_matrix, threshold_vector = get_connection_flux_matrices(c1)
assert leak_matrix.shape == synaptic_matrix.shape
assert synaptic_matrix.shape[0] == threshold_vector.shape[0]
from dipde.internals.internalpopulation import InternalPopulation from dipde.internals.connection import Connection from dipde.interfaces.access_matrices import get_leak_matrix, get_connection_flux_matrices import numpy as np import numpy.linalg as npla import logging logging.disable(logging.CRITICAL) # Components: i1 = InternalPopulation(tau_m=.02, v_min=0, v_max=.02, dv=.001) c1 = Connection(None, i1, 1, weights=.005) # Get matrices: leak_matrix = get_leak_matrix(i1) synaptic_matrix, threshold_vector = get_connection_flux_matrices(c1) A = leak_matrix + 100 * synaptic_matrix A[0, :] = 1 b = np.zeros(A.shape[0]) b[0] = 1 # Solve for steady state: p_star = npla.solve(A, b) # Steady state firing rate print np.dot(p_star, 100 * threshold_vector) # A2 = leak_matrix + 100./(1-np.dot(p_star, threshold_vector))*synaptic_matrix # w, vl = npla.eig(A2) # # # print w[np.argmin(np.abs(w))]
i1_i1 = Connection(i1, i1, 0, weights=wi, delays=0.0)
def cheb(N):
x = np.cos(np.pi * np.arange(N + 1) / N)
c = np.array([2] + [1] *
(N - 1) + [2]) * np.array([(-1)**ii for ii in range(N + 1)])
X = npm.repmat(x, 1, N + 1).reshape(N + 1, N + 1).T
dX = X - X.T
D = (np.outer(c, 1. / c)) / (dX + (np.eye(N + 1))
) # % off-diagonal entries
return D - np.diag(np.sum(
D, axis=1)) #, x#; % diagonal entries
leak_matrix = get_leak_matrix(i1, sparse=False)
synaptic_matrix_bg, threshold_vector_bg = get_connection_flux_matrices(
b1_i1, sparse=False)
synaptic_matrix_recc, _ = get_connection_flux_matrices(i1_i1, sparse=False)
A = L + (nsyn_bg * bgfr + nsyn_01 * f0_ss) * Se + nsyn_11 * f1_ss * Si
A[0, :] = 1
b = np.zeros(A.shape[0])
b[0] = 1
p_star = npla.solve(A, b)
A0 = leak_matrix + (nsyn_bg * bgfr +
nsyn_01 * f0_ss) * synaptic_matrix_bg + nsyn_11 * (
nsyn_bg * bgfr + nsyn_01 * f0_ss) * np.dot(
p_star, threshold_vector_bg) * synaptic_matrix_recc
A1 = (nsyn_bg * bgfr + nsyn_01 * f0_ss) * nsyn_11 * np.outer(
synaptic_matrix_recc.dot(p_star), threshold_vector_bg)
n = A0.shape[0]
from dipde.internals.internalpopulation import InternalPopulation from dipde.internals.connection import Connection from dipde.interfaces.access_matrices import get_leak_matrix, get_connection_flux_matrices import numpy as np import numpy.linalg as npla import logging logging.disable(logging.CRITICAL) # Components: i1 = InternalPopulation(tau_m=.02, v_min=0, v_max=.02, dv=.001) c1 = Connection(None, i1, 1, weights=.005) # Get matrices: leak_matrix = get_leak_matrix(i1) synaptic_matrix, threshold_vector = get_connection_flux_matrices(c1) A = leak_matrix + 100*synaptic_matrix A[0,:] = 1 b = np.zeros(A.shape[0]) b[0]=1 # Solve for steady state: p_star = npla.solve(A,b) # Steady state firing rate print np.dot(p_star, 100*threshold_vector)
dv = .0001
nsyn_bg = 1
bgfr = 600
weight = .03
nsyn_recc = 30 # 16
# Components:
b1 = ExternalPopulation(bgfr, record=True)
i1 = InternalPopulation(tau_m=.05, v_min=0, v_max=1, dv=dv, update_method = 'gmres')
b1_i1 = Connection(b1, i1, nsyn_bg, weights=weight, delays=0.0)
i1_i1 = Connection(i1, i1, nsyn_recc, weights=weight, delays=0.0)
# Get matrices:
leak_matrix = get_leak_matrix(i1, sparse=True)
# leak_matrix = spsp.csr_matrix(leak_matrix.shape)
synaptic_matrix, threshold_vector = get_connection_flux_matrices(b1_i1, sparse=True)
def f(ss_fr_guess):
A = leak_matrix + (nsyn_bg*bgfr+nsyn_recc*ss_fr_guess)*synaptic_matrix
A[0,:] = 1
b = np.zeros(A.shape[0])
b[0]=1
# Compute initial guesses for eigenvector and eigenvalue:
# # Components:
b1 = ExternalPopulation(bgfr, record=True)
i1 = InternalPopulation(tau_m=.05, v_min=0, v_max=1, dv=dv, update_method = 'gmres')
b1_i1 = Connection(b1, i1, nsyn_bg, weights=we, delays=0.0)
i1_i1 = Connection(i1, i1, 0, weights=wi, delays=0.0)
def cheb(N):
x = np.cos(np.pi*np.arange(N+1)/N)
c = np.array([2] + [1]*(N-1) + [2])*np.array([(-1)**ii for ii in range(N+1)])
X = npm.repmat(x,1,N+1).reshape(N+1,N+1).T
dX = X-X.T
D = (np.outer(c,1./c))/(dX+(np.eye(N+1)))# % off-diagonal entries
return D - np.diag(np.sum(D, axis=1))#, x#; % diagonal entries
leak_matrix = get_leak_matrix(i1, sparse=False)
synaptic_matrix_bg, threshold_vector_bg = get_connection_flux_matrices(b1_i1, sparse=False)
synaptic_matrix_recc, _ = get_connection_flux_matrices(i1_i1, sparse=False)
A = L + (nsyn_bg*bgfr+nsyn_01*f0_ss)*Se + nsyn_11*f1_ss*Si
A[0,:] = 1
b = np.zeros(A.shape[0])
b[0]=1
p_star = npla.solve(A,b)
A0 = leak_matrix + (nsyn_bg*bgfr+nsyn_01*f0_ss)*synaptic_matrix_bg + nsyn_11*(nsyn_bg*bgfr+nsyn_01*f0_ss)*np.dot(p_star,threshold_vector_bg)*synaptic_matrix_recc
A1 = (nsyn_bg*bgfr+nsyn_01*f0_ss)*nsyn_11*np.outer(synaptic_matrix_recc.dot(p_star), threshold_vector_bg)
n = A0.shape[0]
N=6
D=-cheb(N-1)*2/delay
tmp1 = np.kron(D[:N-1,:], np.eye(n))
tmp2 = np.hstack((A1,np.zeros((n,(N-2)*n)), A0))
tmp3 = spsp.csr_matrix(np.vstack((tmp1, tmp2)))
